60 citations · 768 across the 56 of their papers we have counts for
57 papers
Cellular diagonals of permutahedra
Bérénice Delcroix-Oger, Guillaume Laplante-Anfossi, Vincent Pilaud +1
We provide a systematic enumerative and combinatorial study of geometric cellular diagonals on the permutahedra. In the first part of the paper, we study the combinatorics of certa…
Hochschild polytopes
Vincent Pilaud, Daria Poliakova
The -multiplihedron is a polytope whose faces correspond to -painted -trees, and whose oriented skeleton is the Hasse diagram of the rotation lattice on binary -pai…
Celebrating Loday's Associahedron
Vincent Pilaud, Francisco Santos, Günter M. Ziegler
We survey Jean-Louis Loday's vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry and algebra. We present in particular four…
Lattices of acyclic pipe dreams
Nantel Bergeron, Noémie Cartier, Cesar Ceballos +1
We show that for any permutation , the increasing flip graph on acyclic pipe dreams with exiting permutation is a lattice quotient of the interval of the weak order.…
Refined product formulas for Tamari intervals
Alin Bostan, Frédéric Chyzak, Vincent Pilaud
We provide short product formulas for the -vectors of the canonical complexes of the Tamari lattices and of the cellular diagonals of the associahedra.
Edge connectivity of simplicial polytopes
Vincent Pilaud, Guillermo Pineda-Villavicencio, Julien Ugon
We show that the graph of a simplicial polytope of dimension has no nontrivial minimum edge cut with fewer than edges, hence the graph is …
Pebble trees
Vincent Pilaud
A pebble tree is an ordered tree where each node receives some colored pebbles, in such a way that each unary node receives at least one pebble, and each subtree has either one mor…
Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra
Frédéric Chapoton, Vincent Pilaud
We introduce the shuffle of deformed permutahedra (a.k.a. generalized permutahedra), a simple associative operation obtained as the Cartesian product followed by the Minkowski sum…
Deformed graphical zonotopes
Arnau Padrol, Vincent Pilaud, Germain Poullot
We study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studied in r…
Acyclic reorientation lattices and their lattice quotients
Vincent Pilaud
We prove that the acyclic reorientation poset of a directed acyclic graph is a lattice if and only if the transitive reduction of any induced subgraph of is a forest. We th…
The canonical complex of the weak order
Doriann Albertin, Vincent Pilaud
We define and study the canonical complex of a finite semidistributive lattice . It is the simplicial complex on the join or meet irreducible elements of which encodes each…
Edge connectivity of simplicial polytopes
Guillermo Pineda-Villavicencio, Julien Ugon
A simplicial polytope is a polytope with all its facets being combinatorially equivalent to simplices. We deal with the edge connectivity of the graphs of simplicial polytopes. We…
Deformation cones of graph associahedra and nestohedra
Arnau Padrol, Vincent Pilaud, Germain Poullot
We give the facet description of the deformation cones of graph associahedra and nestohedra, generalizing the classical parametrization of the family of deformed permutahedra by th…
Shard polytopes
Arnau Padrol, Vincent Pilaud, Julian Ritter
For any lattice congruence of the weak order on permutations, N. Reading proved that gluing together the cones of the braid fan that belong to the same congruence class defines a c…
Removahedral congruences versus permutree congruences
Doriann Albertin, Vincent Pilaud, Julian Ritter
The associahedron is classically constructed as a removahedron, i.e. by deleting inequalities in the facet description of the permutahedron. This removahedral construction extends…
The facial weak order on hyperplane arrangements
Aram Dermenjian, Christophe Hohlweg, Thomas McConville +1
We extend the facial weak order from finite Coxeter groups to central hyperplane arrangements. The facial weak order extends the poset of regions of a hyperplane arrangement to all…
Associahedra for finite type cluster algebras and minimal relations between -vectors
Arnau Padrol, Yann Palu, Vincent Pilaud +1
We show that the mesh mutations are the minimal relations among the -vectors with respect to any initial seed in any finite type cluster algebra. We then use this a…
Signaletic operads
Florent Hivert, Vincent Pilaud
We introduce -signaletic operads and their Koszul duals, generalizing the dendriform, diassociative and duplicial operads (which correspond to the case). We show that the…
Cambrian triangulations and their tropical realizations
Vincent Pilaud
This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on -Tamari lattices and their tropical realizations. For any signature $\varepsil…
Non-kissing and non-crossing complexes for locally gentle algebras
Yann Palu, Vincent Pilaud, Pierre-Guy Plamondon
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, or…
The Hopf algebra of integer binary relations
Vincent Pilaud, Viviane Pons
We construct a Hopf algebra on integer binary relations that contains under the same roof several well-known Hopf algebras related to the permutahedra and the associahedra: the Mal…
Hopf dreams and diagonal harmonics
Nantel Bergeron, Cesar Ceballos, Vincent Pilaud
This paper introduces a Hopf algebra structure on a family of reduced pipe dreams. We show that this Hopf algebra is free and cofree, and construct a surjection onto a commutative…
The weak order on Weyl posets
Joël Gay, Vincent Pilaud
We define a natural lattice structure on all subsets of a finite root system that extends the weak order on the elements of the corresponding Coxeter group. For crystallographic ro…
Hopf algebras on decorated noncrossing arc diagrams
Vincent Pilaud
Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general meth…